This paper proposes a quasi-static conformal mapping analysis to analytically evaluate the input resistance of Archimedean spiral antenna at its radiation region. The deviation from the original constructs of band theory for two-wire spiral antennas leads to the concept of common slot-line mode radiation. The per-unit-length capacitance and the characteristic impedance of the quasi-TEM fundamental propagating mode in periodic coplanar waveguide (PCPW) structure are obtained in terms of spiral parameters including substrate properties. This formula enables little computational effort on the computation of input resistance at the radiation mode of balanced-excited two-arm Archimedean spiral antennas. The numerical simulation demonstrates the accuracy of derived formulas both in free space and when a dielectric layer is presented.
The Archimedean spiral continues to be a widely studied antenna topology thanks to its broadband impedance and radiation characteristics. These have been investigated experimentally and computationally since their initial development in the late 1950s [1,2], and a number of numerical methods have been developed and utilized in the decades following their introduction to model these broadband attributes. Examples of this include the method of moments based on a thin-wire assumption [3,4], finite-volume time-domain (FVTD) [
While these methods have no doubt been collectively successful in their own right, the pursuit of a physically descriptive and rigorous analytical analysis of the Archimedean spiral antenna has in many ways received less attention. This is especially true with regards to the input resistance of the structure. A semi-circular model was first proposed in 1960 [
It is commonly accepted that the basic operation of the Archimedean spiral can be accurately explained using band theory [
In this work, a conformal mapping approach is proposed to derive quasi-static closed-form solutions for the characteristic impedances of PCPW, which is used to characterize the input resistance of the balanced two-arm Archimedean spiral antenna operating in its radiation region. For completeness, the radiating mechanism of spiral antenna is reviewed first along with its geometry. This leads to the development of a model for the PCPW assuming the conductor is of negligible thickness. The mapping between physical and finite image domains is discussed next as a more straightforward approach towards deriving the input resistance of the spiral. A comparison is then made with full-wave electromagnetic solutions to validate the accuracy of this approach over a wide range of design parameters. A brief summary on the conformal mapping and resulting characterization of the spiral concludes the discussion.